Some properties of almost summing operators

[摘要] In this paper we extend the scope of three important results in the linear theory of absolutely summing operators. The first one was obtained by Bu and Kranz in [4] and it asserts that a continuous linear operator between Banach spaces takes almost unconditionally summable sequences into Cohen strongly q-summable sequences for any q > 2, whenever its adjoint is p-summing for some p > 1. The second of them states that p-summing operators with hilbertian domain are Cohen strongly q-summing operators (1 < p, q < 00), this result is due to Bu [3]. The third one is due to Kwapien [8] and it characterizes spaces isomorphic to a Hilbert space using 2-summing operators. We will show that these results are maintained replacing the hypothesis of the operator to be p-summing by almost summing. We will also give an example of an almost summing operator that fails to be p-summing for every 1 < p < 00. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Absolutely p-summing operators;Cohen strongly p-summing operators;Almost p-summing operators